This chapter presents an image gradient based approach to perform 2D and 3D deformable model segmentation using level set. The 2D method uses an external force field that is based on magnetostatics and hypothesized magnetic interactions between the active contour and object boundaries. The major contribution of the method is that the interaction of its forces can greatly improve the active contour in capturing complex geometries and dealing with difficult initializations, weak edges and broken boundaries. This method is then generalized to 3D by reformulating its external force based on geometrical interactions between the relative geometries of the deformable model and the object boundary characterized by image gradient. The evolution of the deformable model is solved using the level set method so that topological changes are handled automatically. The relative geometrical configurations between the deformable model and the object boundaries contribute to a dynamic vector force field that changes accordingly as the deformable model evolves. The geometrically induced dynamic interaction force has been shown to greatly improve the deformable model performance in acquiring complex geometries and highly concave boundaries, and it gives the deformable model a high invariancy in initialization configurations. The voxel interactions across the whole image domain provide a global view of the object boundary representation, giving the external force a long attraction range. The bidirectionality of the external force field allows the new deformable model to deal with arbitrary cross-boundary initializations, and facilitates the handling of weak edges and broken boundaries.

Kernel learning algorithms are currently becoming a standard tool in the area of machine learning and pattern recognition.
In this chapter we review the fundamental theory of kernel learning. As the basic building block we introduce the kernel function,
which provides an elegant and general way to compare possibly very complex objects. We then review the concept
of a reproducing kernel Hilbert space and state the representer theorem. Finally we give an overview of the most
prominent algorithms, which are support vector classification and regression, Gaussian Processes and kernel principal analysis.
With multiple kernel learning and structured output prediction we also introduce some more recent advancements in the field.

Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems